In the sentence
I let him take the pen.
are the following mentioned functions correct?
I = subject
let = main verb
him = indirect Object
take = the second verb (bare infinitive)
the pen = Direct Object
I = main subject.
let = main verb.
him = direct object of let, and subject of take.
take = subordinate verb. It's infinitive because its subject is a direct object.
the pen = direct object of subordinate verb.
If my memory serves me well, let is a transitive verb, "him" is a direct object.